Another thing which intrigues me is that do these functions have an algebraic expression for them, behind the sine or cosine or tangent button on the calculator? Do they have any reality besides being a computer program? I mean that I can just plot a u-shaped parabola and program it into a computer as a function called, say, pine. On the Cartesian graph it is called y=pin (x). Whatever number you type for x will give a certain value of y until you end up with the aforementioned parabola, which really is just a graph of y=x^2 .Someone might ask so how do you compute y from x. Meaning the operations done on a value of x to obtain y, like powers, addition, multiplication, any constants...... This is what I am asking. For sin (x) do you have an expression with such operations whereby I can obtain the correct value of why, without using a calculator?